Mathematical modeling of Breastfeeding's protective effects against HFMD in northern Thailand

Volume 41, Issue 1, pp 114--131 https://dx.doi.org/10.22436/jmcs.041.01.08

Publication Date: September 25, 2025 Submission Date: July 16, 2024 Revision Date: January 27, 2025 Accteptance Date: August 08, 2025

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Authors

S. E. Shuaib - Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000, Thailand. I. Chesu - Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000, Thailand. A. Intarasit - Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000, Thailand. P. Riyapan - Department of Mathematics and Computer Science, Faculty of Science and Technology, Prince of Songkla University, Pattani, 94000, Thailand.

Abstract

According to the World Health Organization’s guidelines, a two-year breastfeeding period is strongly recommended, with research demonstrating its significant benefits in reducing childhood illnesses and mortality rates. Acknowledging this evidence, this study aims to explore this recommendation by focusing on a specific infection, namely Hand, Foot, and Mouth Disease (HFMD). We do so by extending and analyzing an SEIR epidemic model uniquely designed for HFMD transmission and how it affects regional residency in Thailand. The proposed model examines two equilibria: disease-free and endemic, revealing local and global stability conditions determined by the basic reproduction number (\( R_{\rm bfeed} \)). Our analysis includes global stability for both disease-free and endemic equilibrium points, using a quadratic Lyapunov function for the global stability assessment of the endemic point. Additionally, we conducted a sensitivity analysis of different parameters for the basic reproduction number to enhance our understanding of model dynamics. Finally, numerical simulations, which include the simulation of general dynamics, examining the impact of breastfeeding, data fitting, model validation, and predicting future HFMD forecasts, were conducted using RStudio and Python software. These simulations help us explore the effects of breastfeeding on HFMD transmission, offering insights into the potential implications for controlling hand, foot, and mouth disease among children in Thailand.

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Keywords

• Breastfeeding
• hand foot, and mouth disease
• mathematical model
• rural and urban provinces

MSC

•  92D30
•  34D20
•  92B05
•  92D25

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